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A192506 Numbers that are neither ludic nor prime.

%I A192506 #28 Dec 10 2021 07:24:54
%S A192506 4,6,8,9,10,12,14,15,16,18,20,21,22,24,26,27,28,30,32,33,34,35,36,38,
%T A192506 39,40,42,44,45,46,48,49,50,51,52,54,55,56,57,58,60,62,63,64,65,66,68,
%U A192506 69,70,72,74,75,76,78,80,81,82,84,85,86,87,88,90,92,93,94
%N A192506 Numbers that are neither ludic nor prime.
%C A192506 Intersection of A002808 and A192607; (1-A010051(a(n)))*(1-A192490(a(n)))=1;
%C A192506 a(n) = A091212(n) for n <= 60.
%C A192506 a(n) = A175526(n) for n <= 53. - _Reinhard Zumkeller_, Jul 12 2011
%C A192506 In other words, composite numbers that are nonludic. - _Antti Karttunen_, May 11 2015
%H A192506 Reinhard Zumkeller (first 1000 terms) & Antti Karttunen, <a href="/A192506/b192506.txt">Table of n, a(n) for n = 1..10000</a>
%t A192506 a3309[nmax_] := a3309[nmax] = Module[{t = Range[2, nmax], k, r = {1}}, While[Length[t] > 0, k = First[t]; AppendTo[r, k]; t = Drop[t, {1, -1, k}]]; r];
%t A192506 ludicQ[n_, nmax_] /; 1 <= n <= nmax := MemberQ[a3309[nmax], n];
%t A192506 terms = 1000;
%t A192506 f[nmax_] := f[nmax] = Select[Range[nmax], !ludicQ[#, nmax] && !PrimeQ[#]&] // PadRight[#, terms]&;
%t A192506 f[nmax = terms];
%t A192506 f[nmax = 2 nmax];
%t A192506 While[f[nmax] != f[nmax/2], nmax = 2 nmax];
%t A192506 seq = f[nmax] (* _Jean-François Alcover_, Dec 10 2021, after _Ray Chandler_ in A003309 *)
%o A192506 (Haskell)
%o A192506 a192506 n = a192506_list !! (n-1)
%o A192506 a192506_list = filter ((== 0) . a010051) a192607_list
%o A192506 (Scheme, with Antti Karttunen's IntSeq-library)
%o A192506 (define A192506 (MATCHING-POS 1 1 (lambda (n) (and (zero? (A192490 n)) (zero? (A010051 n))))))
%o A192506 ;; _Antti Karttunen_, May 07 2015
%Y A192506 Cf. A257689 (complement, either ludic or prime), A192503 (ludic and prime), A192504 (ludic and nonprime), A192505 (nonludic and prime).
%Y A192506 Cf. A010051, A192490, A002808, A192607.
%Y A192506 a(n) differs from A091212(n) and A205783(n+1) for the first time at n=37, where a(37) = 55, while 55 is missing from both A091212 and A205783.
%Y A192506 Differs from A175526 for the first time at n=54, where a(54) = 78, while A175526(54) = 77, a term which is missing from here.
%K A192506 nonn
%O A192506 1,1
%A A192506 _Reinhard Zumkeller_, Jul 05 2011